I installed intel graphic drivers and now can't interact with my system. What can I do?

Question

I have a

System:    Host: *** Kernel: 5.0.0-36-generic x86_64 bits: 64 gcc: 7.4.0 Console: tty 0
           Distro: Ubuntu 18.04.3 LTS
Machine:   Device: desktop Mobo: Micro-Star model: MS-AAC11 v: 1.0 serial: N/A UEFI: American Megatrends v: 8.00 date: 04/18/2017
CPU:       Dual core Intel Core i3-7100 (-MT-MCP-) arch: Skylake rev.9 cache: 3072 KB
           flags: (lm nx sse sse2 sse3 sse4_1 sse4_2 ssse3 vmx) bmips: 15648
           clock speeds: max: 3900 MHz 1: 1143 MHz 2: 3045 MHz 3: 3526 MHz 4: 3560 MHz
Graphics:  Card: Intel HD Graphics 630 bus-ID: 00:02.0
           Display Server: N/A drivers: modesetting (unloaded: fbdev,vesa)
           tty size: 135x47 Advanced Data: N/A out of X

and graphic performance was very poor. So, when I looked at this inxioutput, I realized, that seemingly no intel drivers were loaded. So I had the idea to apt install xserver-xorg-video-intel. This removed quite a bit of other stuff (unfortunately, I did this with apt on a ssh session, so maybe I haven't got the whole output).

(Reading database ... 309003 files and directories currently installed.)
Removing lubuntu-gtk-core (0.94.1) ...
Removing xserver-xorg-input-synaptics-hwe-18.04 (1.9.1-1ubuntu1~18.04.1) ...
Removing xserver-xorg-video-all-hwe-18.04 (1:7.7+19ubuntu8~18.04.2) ...
Removing xserver-xorg-video-amdgpu-hwe-18.04 (19.0.1-1~18.04.1) ...
Removing xserver-xorg-input-wacom-hwe-18.04 (1:0.36.1-0ubuntu1~18.04.1) ...
Removing xserver-xorg-video-vmware-hwe-18.04 (1:13.3.0-2build1~18.04.1) ...
Removing xserver-xorg-video-vesa-hwe-18.04 (1:2.4.0-1~18.04.1) ...
Removing xserver-xorg-input-all (1:7.7+19ubuntu7.1) ...
Removing xserver-xorg-input-libinput-hwe-18.04 (0.28.1-1~18.04.1) ...
Removing xserver-xorg-video-ati-hwe-18.04 (1:19.0.1-0ubuntu1~18.04.1) ...
Removing xserver-xorg-video-fbdev-hwe-18.04 (1:0.5.0-1ubuntu1~18.04.1) ...
Removing xserver-xorg-video-intel-hwe-18.04 (2:2.99.917+git20171229-1ubuntu1~18.04.1) ...
Removing xserver-xorg-video-nouveau-hwe-18.04 (1:1.0.16-1~18.04.1) ...
Removing xserver-xorg-video-qxl-hwe-18.04 (0.1.5-2build2~18.04.1) ...
Removing xserver-xorg-video-radeon-hwe-18.04 (1:19.0.1-0ubuntu1~18.04.1) ...
Removing xserver-xorg-core-hwe-18.04 (2:1.20.4-1ubuntu3~18.04.1) ...
Selecting previously unselected package xserver-xorg-core.
(Reading database ... 308826 files and directories currently installed.)
Preparing to unpack .../xserver-xorg-core_2%3a1.19.6-1ubuntu4.3_amd64.deb ...
Unpacking xserver-xorg-core (2:1.19.6-1ubuntu4.3) ...
Selecting previously unselected package xserver-xorg-video-intel.
Preparing to unpack .../xserver-xorg-video-intel_2%3a2.99.917+git20171229-1_amd64.deb ...
Unpacking xserver-xorg-video-intel (2:2.99.917+git20171229-1) ...
Setting up xserver-xorg-core (2:1.19.6-1ubuntu4.3) ...
Setting up xserver-xorg-video-intel (2:2.99.917+git20171229-1) ...
Processing triggers for man-db (2.8.3-2ubuntu0.1) ...
Processing triggers for libc-bin (2.27-3ubuntu1) ...

Now, the system still boots, but the de login screen does not allow any inputs, neither mouse nor keyboard. The cursor is blinking, though. I cannot reach a tty and I have no network connection (as seen from the router).

Pressing esc during boot brings me to a working grub console, that is the best in interactivity I could evoke. Shift does not seem to do anything, so at least that way I cannot get to a safe boot option or anything alike.

How should I continue from here?